Use MATLAB to write code to solve the problem

find min f(x1,x2,x3,x4) = 0.1x(1)^2+0.4x(2)^2+0.5x(3)^2+0.2x(4)^2+x(1)+2X(2)+3x(3)+x(4)+6

Find min f(x1,x2,x3,x4) and the corresponding values of x1, x2, x3, x4 subject to

2x1 + x2 + 2x3 + x4 = 5
x1 + 2x2 + 4x3 + 5x4 ≤ −21
−18 ≤ x1 ≤ 8
−20 ≤ x2 ≤ 16
−14 ≤ x3 ≤ 13
−15 ≤ x4 ≤ 5

[KSSV]

Read about fmincon

[Tran Paul]

Hi KSSV, I made the code based on fmincon, but it requires the initial point. Can I ask you how to choose the initial point?

[Aquatris]

There is no right or wrong way of choosing initial point, as long as initial point satisfies the constraints. One method is to solve the problem using different initial points that are randomly chosen and picking the solution that gives you the minimum function value.

Otherwise you can consider using global optimization techniques, such as genetic algorithm and particle swarm optimization.

[Tran Paul]

I got it, thank you so much

Answer 1

[SYED ABOU ILTAF HUSSAIN]

here is the code for your problem

[Tran Paul]

Thank you so much. But I want to ask you why don't we made the code following the linear equality and inequality constraints. Either your codes or my code, we got the same solutions.

if true
  % code
end